Eulerian Polynomials, Stirling Permutations of the Second Kind and Perfect Matchings

Shi-Mei Ma, Yeong-Nan Yeh

Abstract


In this paper, we introduce Stirling permutations of the second kind. In particular, we count Stirling permutations of the second kind by their cycle ascent plateaus, fixed points and cycles. Moreover, we get an expansion of the ordinary derangement polynomials in terms of the Stirling derangement polynomials. Finally, we present constructive proofs of a kind of combinatorial expansions of the Eulerian polynomials of types $A$ and $B$.

Keywords


Eulerian polynomials; Stirling permutations of the second kind; Stirling derangements

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